Now showing 1 - 10 of 12
  • Publication
    Cryptanalysis of optical security systems with significant output images
    The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements to heuristically estimate the phase key in the Fourier domain by several plaintext-cyphertext pairs. We obtain correlation output images with very low error by correlating the estimated key with corresponding random phase masks. Our studies show that the convergence behavior of this algorithm sensitively depends on the starting point. We also demonstrate that this algorithm can be used to attack the double random phase encoding technique.
    Scopus© Citations 87  539
  • Publication
    Spread-space spread-spectrum technique for secure multiplexing
    A novel technique for multiplexing complex images is proposed in which each image may be demultiplexed only if a set of random encryption keys is known. The technique utilizes the ability of the double random phase encoding method to spread a signals’ energy in both the space and the spatial frequency domains in a controlled manner. To multiplex, images are independently encrypted with different phase keys and then superimposed by recording sequentially on the same material. Each image is extracted by using the particular key associated with it. During decryption the energy from the other images is further spread, making it possible to minimize its effects by using suitable filters. Wigner analysis is applied to the technique, and numerical results are presented.
    Scopus© Citations 51  477
  • Publication
    Controlling speckle using lenses and free space
    The correlation properties of speckle fields are studied for general paraxial systems. The previous studies on lateral and longitudinal speckle size for the case of free-space propagation (Fresnel transform) are generalized to the case of the linear canonical transform. These results have implications for the control of speckle size, through appropriate design of optical systems, with particular relevance for speckle interferometry.
      419Scopus© Citations 17
  • Publication
    Noninterferometric phase retrieval using a fractional Fourier system
    The signal extraction method based on intensity measurements in two close fractional Fourier domains is examined by using the phase space formalism. The fractional order separation has a lower bound and an upper bound that depend on the signal at hand and the noise in the optical system used for measurement. On the basis of a theoretical analysis, it is shown that for a given optical system a judicious choice of fractional order separation requires some a priori knowledge of the signal bandwidth. We also present some experimental results in support of the analysis.
    Scopus© Citations 27  473
  • Publication
    Paraxial speckle-based metrology systems with an aperture
    Digital speckle photography can be used in the analysis of surface motion in combination with an optical linear canonical transform (LCT). Previously [D. P. Kelly et al. Appl. Opt. 44, 2720 (2005)] it has been shown that optical fractional Fourier transforms (OFRTs) can be used to vary the range and sensitivity of speckle-based metrology systems, allowing the measurement of both the magnitude and direction of tilting (rotation) and translation motion simultaneously, provided that the motion is captured in two separate OFRT domains. This requires two bulk optical systems. We extend the OFRT analysis to more general LCT systems with a single limiting aperture. The effect of a limiting aperture in LCT systems is examined in more detail by deriving a generalized Yamaguchi correlation factor. We demonstrate the benefits of using an LCT approach to metrology design. Using this technique, we show that by varying the curvature of the illuminating field, we can effectively change the output domain. From a practical perspective this means that estimation of the motion of a target can be achieved by using one bulk optical system and different illuminating conditions. Experimental results are provided to support our theoretical analysis.
    Scopus© Citations 24  479
  • Publication
    Generalized Yamaguchi correlation factor for coherent quadratic phase speckle metrology systems with an aperture
    In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed decorrelation effects that ultimately define this range are described by the well-known Yamaguchi correlation factor. We extend this result to all coherent quadratic phase paraxial optical systems with a single aperture and provide experimental results to support our theoretical conclusions.
      487Scopus© Citations 15
  • Publication
    Key-space analysis of double random phase encryption technique
    We perform a numerical analysis on the double random phase encryption/decryption technique. The key-space of an encryption technique is the set of possible keys that can be used to encode data using that technique. In the case of a strong encryption scheme, many keys must be tried in any brute-force attack on that technique. Traditionally, designers of optical image encryption systems demonstrate only how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. However, this type of demonstration does not discuss the properties of the key-space nor refute the feasibility of an efficient brute-force attack. To clarify these issues we present a key-space analysis of the technique. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute-force attack.
    Scopus© Citations 86  1600
  • Publication
    Role of phase key in the double random phase encoding technique : an error analysis
    We perform a numerical analysis of the double random phase encryption–decryption technique to determine how, in the case of both amplitude and phase encoding, the two decryption keys (the image- and Fourier-plane keys) affect the output gray-scale image when they are in error. We perform perfect encryption and imperfect decryption. We introduce errors into the decrypting keys that correspond to the use of random distributions of incorrect pixel values. We quantify the effects that increasing amounts of error in the image-plane key, the Fourier-plane key, and both keys simultaneously have on the decrypted image. Quantization effects are also examined
      1257Scopus© Citations 39
  • Publication
    Polarization encoding and multiplexing of two-dimensional signals : application to image encryption
    (Optical Society of America, 2006-08-01) ; ;
    We discuss an optical system that encodes an input signal to a polarization state, using a spatial light modulator (SLM). Using two SLMs the optical system multiplexes two 2D signals in the polarization domain, and we demonstrate the multiplexing of two binary images. The encryption and decryption of two binary images using an XOR operation is also presented.
    Scopus© Citations 61  631
  • Publication
    Statistical investigation of the double random phase encoding technique
    The amplitude-encoding case of the double random phase encoding technique is examined by defining a cost function as a metric to compare an attempted decryption against the corresponding original input image. For the case when a cipher–text pair has been obtained and the correct decryption key is unknown, an iterative attack technique can be employed to ascertain the key. During such an attack the noise in the output field for an attempted decryption can be used as a measure of a possible decryption key’s correctness. For relatively small systems, i.e., systems involving fewer than 5x5 pixels, the output decryption of every possible key can be examined to evaluate the distribution of the keys in key space in relation to their relative performance when carrying out decryption. However, in order to do this for large systems, checking every single key is currently impractical. One metric used to quantify the correctness of a decryption key is the normalized root mean squared (NRMS) error. The NRMS is a measure of the cumulative intensity difference between the input and decrypted images. We identify a core term in the NRMS, which we refer to as the difference parameter, d. Expressions for the expected value (or mean) and variance of d are derived in terms of the mean and variance of the output field noise, which is shown to be circular Gaussian. These expressions assume a large sample set (number of pixels and keys). We show that as we increase the number of samples used, the decryption error obeys the statistically predicted characteristic values. Finally, we corroborate previously reported simulations in the literature by using the statistically derived expressions.
      1018Scopus© Citations 18